A Continuous and Interpretable Morphometric for Robust Quantification of Dynamic Biological Shapes

MCML Authors

Juan-Esteban Suarez Cardona

Dr.

→ Group Gitta Kutyniok
 Mathematical Foundations of Artificial Intelligence

Abstract

We introduce the Push-Forward Signed Distance Morphometric (PF-SDM) for shape quantification in biomedical imaging. The PF-SDM compactly encodes geometric and topological properties of closed shapes, including their skeleton and symmetries. This provides robust and interpretable features for shape comparison and machine learning. The PF-SDM is mathematically smooth, providing access to gradients and differential-geometric quantities. It also extends to temporal dynamics and allows fusing spatial intensity distributions, such as genetic markers, with shape dynamics. We present the PF-SDM theory, benchmark it on synthetic data, and apply it to predicting body-axis formation in mouse gastruloids, outperforming a CNN baseline in both accuracy and speed.

misc RSV+25

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Preprint

Oct. 2025

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Authors

R. Rouatbi • J.-E. Suarez Cardona • A. Villaronga-Luque • J. V. Veenvliet • I. F. Sbalzarini

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Links

arXiv

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In Collaboration

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Research Area

 A2 | Mathematical Foundations